Nonlinear dynamics of coupled transverse-rotational waves in granular chains

Zhang, Q; Umnova, O; Venegas, R

Abstract

The nonlinear dynamics of coupled waves in one-dimensional granular chains with and without a substrate
is theoretically studied accounting for quadratic nonlinearity. The multiple time scale method is used to derive
the nonlinear dispersion relations for infinite granular chains and to obtain the wave solutions for semiinfinite
systems. It is shown that the sum-frequency and difference-frequency components of the coupled
transverse-rotational waves are generated due to their nonlinear interactions with the longitudinal wave.
Nonlinear resonances are not present in the chain with no substrate where these frequency components have
low amplitudes and exhibit beating oscillations. In the chain positioned on a substrate two types of nonlinear
resonances are predicted. At resonance, the fundamental frequency wave amplitudes decrease and the
generated frequency component amplitudes increase along the chain, accompanied by the oscillations due to
the wave numbers asynchronism. The results confirm the possibility of a highly efficient energy transfer
between the waves of different frequencies, which could find applications in the design of acoustic devices
for energy transfer and energy rectification.

Citation

Zhang, Q., Umnova, O., & Venegas, R. (2019). Nonlinear dynamics of coupled transverse-rotational waves in granular chains. Physical Review E, 100(6), 062206. https://doi.org/10.1103/PhysRevE.100.062206

• Journal Article Type: Article
• Acceptance Date: Nov 30, 2019
• Online Publication Date: Dec 19, 2019
• Publication Date: Dec 19, 2019
• Deposit Date: Mar 2, 2020
• Publicly Available Date: Mar 2, 2020
• Journal: Physical Review E (PRE)
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Volume: 100
• Issue: 6
• Pages: 062206
• DOI: https://doi.org/10.1103/PhysRevE.100.062206
• Publisher URL: https://doi.org/10.1103/PhysRevE.100.062206
• Related Public URLs: https://journals.aps.org/pre/